Stabilization of Galerkin approximations of transport equations by subgrid modeling

Jean-Luc Guermond

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 33, Issue: 6, page 1293-1316
  • ISSN: 0764-583X

Abstract

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This paper presents a stabilization technique for approximating transport equations. The key idea consists in introducing an artificial diffusion based on a two-level decomposition of the approximation space. The technique is proved to have stability and convergence properties that are similar to that of the streamline diffusion method.

How to cite

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Guermond, Jean-Luc. "Stabilization of Galerkin approximations of transport equations by subgrid modeling." ESAIM: Mathematical Modelling and Numerical Analysis 33.6 (2010): 1293-1316. <http://eudml.org/doc/197572>.

@article{Guermond2010,
abstract = { This paper presents a stabilization technique for approximating transport equations. The key idea consists in introducing an artificial diffusion based on a two-level decomposition of the approximation space. The technique is proved to have stability and convergence properties that are similar to that of the streamline diffusion method. },
author = {Guermond, Jean-Luc},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = { Linear hyperbolic equations; hierarchical finite elements; stabilization; subgrid modeling; artificial viscosity.; stabilization; transport equations; artificial diffusion; stability; convergence; streamline diffusion method},
language = {eng},
month = {3},
number = {6},
pages = {1293-1316},
publisher = {EDP Sciences},
title = {Stabilization of Galerkin approximations of transport equations by subgrid modeling},
url = {http://eudml.org/doc/197572},
volume = {33},
year = {2010},
}

TY - JOUR
AU - Guermond, Jean-Luc
TI - Stabilization of Galerkin approximations of transport equations by subgrid modeling
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 33
IS - 6
SP - 1293
EP - 1316
AB - This paper presents a stabilization technique for approximating transport equations. The key idea consists in introducing an artificial diffusion based on a two-level decomposition of the approximation space. The technique is proved to have stability and convergence properties that are similar to that of the streamline diffusion method.
LA - eng
KW - Linear hyperbolic equations; hierarchical finite elements; stabilization; subgrid modeling; artificial viscosity.; stabilization; transport equations; artificial diffusion; stability; convergence; streamline diffusion method
UR - http://eudml.org/doc/197572
ER -

Citations in EuDML Documents

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  1. Erik Burman, Alexandre Ern, Implicit-explicit Runge–Kutta schemes and finite elements with symmetric stabilization for advection-diffusion equations
  2. Erik Burman, Alexandre Ern, Implicit-explicit Runge–Kutta schemes and finite elements with symmetric stabilization for advection-diffusion equations
  3. Gunar Matthies, Piotr Skrzypacz, Lutz Tobiska, A unified convergence analysis for local projection stabilisations applied to the Oseen problem
  4. Erik Burman, Alexandre Ern, Implicit-explicit Runge–Kutta schemes and finite elements with symmetric stabilization for advection-diffusion equations
  5. Malte Braack, A stabilized finite element scheme for the Navier-Stokes equations on quadrilateral anisotropic meshes
  6. Sébastien Boyaval, Tony Lelièvre, Claude Mangoubi, Free-energy-dissipative schemes for the Oldroyd-B model

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